Acquia Dev Desktop is currently not compatible with MacOS 10.15 Catalina. We are waiting on a third-party to validate the 64-bit application that will make it compatible. Watch our release notes to find out when we have an update version.
Previous versions of MacOS (that is, previous to Catalina) alert with this text:
This app will not work with future versions of macOS and needs to be updated to improve compatibility. Contact the developer for more information.
Acquia is the developer of Dev Desktop, and as stated above, we are awaiting validation and will release an updated version as soon as we get that. If you are able to hold off on upgrading to Catalina, then Dev Desktop will work, just with an alert to start.